There are two points A and B on the 1. plane, and AB = 2cm. If point A is the center of rotation and point B rotates by 3 6 0, then the rotated figure is _ _ _ _ _.

2. The area of two centrally symmetric figures is _ _ _ _ _ _ _ _.

3. In the parallelogram ABCD, AC and BD intersect at O. If AB = 4cm, the ratio of the length of AD to the length of AB is 3: 2, and the circumference of △BOC is 24cm, then AC+BD = _ _ _ _ _.

4. If the perimeter of the parallelogram is 36 cm and the ratio of two adjacent sides is 5: 4, the length of the two adjacent sides is _ _ _ _ _.

5. In the parallelogram ABCD, if the sum of complementary angles of ∠A and ∠B is 200, ∠ A = _ _ _ _

6. In the diamond ABCD, if AB = 16cm, ∠ABC= 120, the diagonal BD = _ _ _ _.

7. The included angle between the two diagonals of a rectangle is 120, and the sum of the lengths is 24 cm, so the length of the short side of the rectangle is _ _ _ _ _.

8. In a square ABCD, where P is any point of AD, PE⊥AC, PF⊥BD, E and F are vertical feet respectively, and BD+AC = 14cm, then PE+PF = _ _ _ _

9.e is a point in the square ABCD, and △ABE is a regular triangle, then ∠ DEC = _ _ _ _ _.

10. If a diagonal of an isosceles trapezoid is perpendicular to a waist, and the length of the upper and lower sides is equal to the length of the waist, the degree of each internal angle of the isosceles trapezoid is _ _ _ _ _ _.

Second, multiple-choice questions (3 points for each small question, * * * 1.2 points)

1 1. The following statement is wrong ().

(a) The center of symmetry of a centrally symmetric figure must be located at the midpoint of a line segment connecting two points on the figure.

(b) In the parallelogram ABCD, if o is the intersection of AC and BD, then AO=BO.

(c) The line segment is a centrally symmetric figure, and the center of symmetry is its midpoint.

(d) A parallelogram is a figure with a symmetrical center, and its vertex is its symmetrical center.

12. In the parallelogram ABCD, O is any point on the diagonal AC, AC bisects ∠BAD, and the intersection point O is EF‖AB. When it intersects with AD and BC at points E and F respectively, the angle equal to ∠AOE is ().

Five (b) four (c) three (d) two

13. Diamond ().

(a) It is an axisymmetric figure, not a centrally symmetric figure.

(b) It is a centrally symmetric figure, not an axisymmetric figure.

(c) It is neither an axisymmetric figure nor a centrally symmetric figure.

(d) It is both an axisymmetric figure and a centrally symmetric figure.

14. The following propositions cannot be used as the basis for judging isosceles trapezoid ().

(a) In a quadrilateral, one set of opposite sides is parallel but not equal, and the other set is equal.

(b) One set of opposite sides of a quadrilateral is parallel and the other set of opposite sides is equal.

(c) A trapezoid with two equal angles on the same base.

(d) A trapezoid with equal diagonals.

Third, the calculation problem (7 points for each small question, 28 points for * * *)

15. In the parallelogram ABCD, e and f are the midpoint of AD and DC respectively. Find s: S.

16. In right-angle ABCD, AC and BD intersect at O, AE bisects ∠DAB, ∠ACB=30, and the degree of ∠BEO is found.

17. The ratio of the lengths of the two diagonal lines of the diamond is 2: 3, and the sum of their lengths is 50. Find the area of the diamond.

Eighteen floors ... If the angle formed by the intersection of two diagonal lines of a rectangle is 70, find the angle formed by the diagonal line and a group of adjacent sides of the rectangle.

4. Short answer questions (each question 1 0)

19. How many centimeters should the longer diagonal of two parallelograms with adjacent sides of 5 cm and 3 cm be less than? How many centimeters should the shorter diagonal be greater than? Why?

20. In the rectangular ABCD, vertex C is the vertical line of diagonal BD, and intersects with the bisector of ∠A at point E. Try to explain that AC = ce.

2 1. In the right triangle ABC, ∠ACB = 90, CD bisects ∠ ACB, intersecting with AB at point D, intersecting with DE⊥BC at point E, and intersecting with DF⊥AC at point F. Try to explain that the quadrilateral DECF is a square.

References:

Beijing Normal University website

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